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all three perpendicular bisectors elongate to meet at the incenter of the triangle.

Q: The perpendicular bisectors of a triangle all pass through what point?

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The circumcenter, the incenter is the point of concurrency of the angle bisectors of a triangle.

Since the intersection of the perpendicular bisectors of a triangle is the center of the inscribed circle (we call it the centroid of a triangle), the answer is no.

The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.

The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.

intersection

Related questions

The circumcenter, the incenter is the point of concurrency of the angle bisectors of a triangle.

Since the intersection of the perpendicular bisectors of a triangle is the center of the inscribed circle (we call it the centroid of a triangle), the answer is no.

It is the circumcentre.

circumcenter

circumcenter

The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.

The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.

circumcenter

Circumcenter.

intersection

inscribed

y